Summary of New Features in Mathematica 8 (Mathematica Guide)

Quasi-Newton Methods (Mathematica Tutorial)

There are many variants of quasi-Newton methods. In all of them, the idea is to base the matrix B_k in the quadratic model on an approximation of the Hessian matrix built up ...

Efficiency (Compiled Function Tools Tutorial)

This section is designed to discuss how to make compiled functions run efficiently. It will cover features that make them run faster, as well as problems that can make them ...

EngineeringForm (Built-in Mathematica Symbol)

EngineeringForm[expr] prints with all real numbers in expr given in engineering notation. EngineeringForm[expr, n] prints with numbers given to n-digit precision.

PaddedForm (Built-in Mathematica Symbol)

PaddedForm[expr, n] prints with all numbers in expr padded to leave room for a total of n digits. PaddedForm[expr, {n, f}] prints with approximate real numbers having exactly ...

ScientificForm (Built-in Mathematica Symbol)

ScientificForm[expr] prints with all real numbers in expr given in scientific notation. ScientificForm[expr, n] prints with numbers given to n-digit precision.

Flat and Orderless Functions (Mathematica Tutorial)

Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

Quantifiers (Mathematica Tutorial)

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...

Introduction to Step Control (Mathematica Tutorial)

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

PDF (Built-in Mathematica Symbol)

PDF[dist, x] gives the probability density function for the symbolic distribution dist evaluated at x.PDF[dist, {x_1, x_2, ...}] gives the multivariate probability density ...